An age-structured epidemic model for the demographic transition.
Hisashi Inaba1, Ryohei Saito2, Nicolas Bacaër3
1Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan. inaba@ms.u-tokyo.ac.jp.
Journal of Mathematical Biology
|August 2, 2018
Summary
This study models demographic transition by treating cultural norm transmission as an epidemic. It proves the model
Area of Science:
- Mathematical epidemiology
- Demographic modeling
- Dynamical systems
Background:
- Demographic transition involves declining fertility rates.
- Cultural norms influence fertility decisions.
- Modeling disease spread can inform social dynamics.
Purpose of the Study:
- To develop an age-structured epidemic model for demographic transition.
- To analyze the transmission of cultural norms as an infectious process.
- To investigate the mathematical properties and stability of the model.
Main Methods:
- Formulation of an abstract homogeneous Cauchy problem on a Banach space.
- Analysis of existence, uniqueness, and well-posedness of solutions.
- Investigation of nontrivial exponential solutions and their stability using asynchronous exponential growth.
- Examination of relative and absolute stability.
- Formulation of stability conditions using reproduction numbers for boundary solutions.
Main Results:
- Existence and uniqueness of solutions for the age-structured epidemic model.
- Identification of conditions for nontrivial exponential solutions.
- Analysis of the stability of exponential solutions, including boundary cases (infection-free/totally infected).
- Demonstration that bi-unstability of boundary solutions can lead to coexistent exponential solutions.
Conclusions:
- The age-structured epidemic model provides a framework for understanding demographic transition through cultural norm transmission.
- Mathematical analysis confirms the existence and stability properties of model solutions.
- Reproduction numbers are key to determining the stability of simplified states and the emergence of complex dynamics.
Related Concept Videos
02:31Phase Transitions
23.2K
Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to...
23.2K
01:58Cooperative Allosteric Transitions
8.8K
Cooperative allosteric transitions can occur in multimeric proteins, where each subunit of the protein has its own ligand-binding site. When a ligand binds to any of these subunits, it triggers a conformational change that affects the binding sites in the other subunits; this can change the affinity of the other sites for their respective ligands. The ability of the protein to change the shape of its binding site is attributed to the presence of a mix of flexible and stable segments in the...
8.8K
02:58Properties of Transition Metals
29.9K
Transition metals are defined as those elements that have partially filled d orbitals. As shown in Figure 1, the d-block elements in groups 3–12 are transition elements. The f-block elements, also called inner transition metals (the lanthanides and actinides), also meet this criterion because the d orbital is partially occupied before the f orbitals.
29.9K
02:39Phase Transitions: Vaporization and Condensation
21.5K
The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize (convert into vapor). The process is called vaporization—a surface phenomenon. Vaporization occurs when the thermal motion of the molecules overcome the intermolecular forces, and the molecules (at the surface) escape into the gaseous state. When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase molecules...
21.5K
02:33Phase Transitions: Sublimation and Deposition
20.2K
Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and standard pressure, a piece of dry ice (solid CO2) sublimes, appearing to gradually disappear without ever forming any liquid. Snow and ice sublimate at temperatures below the melting point of water, a slow process that may be accelerated by winds and the reduced atmospheric pressures at high altitudes. When solid iodine is warmed, the solid sublimes...
20.2K
02:39Phase Transitions: Melting and Freezing
15.2K
Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...
15.2K